Help: BVP4C warning error !!

Hi there, I'm solving a bvp using bvp4c. There is a warning error which I do not understand at all. Can someone please explain what is about and how to solve this problem?

**Warning: Unable to meet the tolerance without using more than 1666 mesh points. The last mesh of 2000 points and the solution are available in the output argument. The maximum residual is 240.083, while requested accuracy is 0.001. **

Many thanks.

Syaza

Answer 1

[Walter Roberson]

Increase NMax.

http://www.mathworks.com/help/matlab/ref/bvpset.html#f79-1034656

[Syaza Latif]

Hi Walter,

I have tried increasing NMax and RelTol but I get the same error. Here is my code:

function mat4bvp_Model

clc

clear all

global beta gamma theta s0 Ri Di Rf Df

% %%~~R=y(1); D=y(2); E=y(3); lambda_R=y(4);lambda_D=y(5);lambda_E=y(6);

%%% the parameter values

beta= 0.7379; Ri=0.6118; Di=0.0164; gamma=0.2801; theta=0.05; s0=0.1;

%%% the pre-defined (fixed) end points for D

Df=0.3483;

options = bvpset('RelTol', 1e-4, 'AbsTol', 1e-4, 'NMax', 10000)

solinit = bvpinit(linspace(0,100),[Ri Di 1.0 0.1 1 0.1]);

sol = bvp4c(@mat4ode_Model,@mat4bc_Model,solinit,options)

t = linspace(0,100,1000);

y = deval(sol,t);

%% plotting the figures

figure(1)

plot(t,y(1,:))

figure(2)

plot(t,y(2,:))

figure(3)

plot(t,y(3,:))

figure(4)

plot(t,y(4,:))

figure(5)

plot(t,y(5,:))

figure(6)

plot(t,y(6,:))

end

%%-the boundary conditions---------------------------------------------------

function res=mat4bc_Model(ya,yb)

global Ri Di Df

res=[ya(1)-Ri

    ya(2)-Di

    yb(2)-Df

    ya(3)

    yb(4)

    yb(6)];

end

%%---the ODEs--------------------------------------------------

function dydx=mat4ode_Model(t,y)

global beta gamma theta s0

% %%~~R=y(1); D=y(2); E=y(3); lambda_R=y(4);lambda_D=y(5);lambda_E=y(6);

dydx=[(y(3)-gamma*y(1))*(1-y(1)-y(2)) %% dR/dt

       beta*y(2)*(1-y(1)-y(2))                                %%dD/dt

       -theta*y(3)+ s0*c(s0,y(6))                             %%dE/dt

       y(4)*(y(3)+gamma* (1-2*y(1)-y(2))) + beta*y(5)*y(2)    %%dlambda_R/dt

       y(4)*(y(3)-gamma*y(1))- y(5)*beta*(1-y(1)-2*y(2))      %%dlambda_D/dt

       y(6)*theta - y(4)*(1-y(1)-y(2))];                      %%dlambda_E/dt

end

function C=c(s0,y6)

C=-s0/2 * y6;

end